Classical Lie Algebras at Infinity

This book is a hybrid text-monograph that bridges a traditional graduate course to research-level representation theory, appropriate for advanced graduate students and research mathematicians. It covers the structure and representation theory of infinite-dimensional locally reductive Lie algebras and superalgebras, with exercises of various levels of difficulty.

Format: Hardback
Length: 239 pages
Publication date: 06 January 2022
Publisher: Springer Nature Switzerland AG

This book, originating from graduate-level courses taught by the first author, serves as a distinctive text-monograph hybrid that seamlessly connects a traditional graduate course to the realm of research-level representation theory. The exposition encompasses an introduction to the subject, notable highlights of the theory, and recent advancements in the field, making it suitable for advanced graduate students embarking on this field as well as research mathematicians seeking to broaden their expertise. The mathematical prerequisites for each chapter vary, but a standard course on Lie algebras and their representations, coupled with a foundational understanding of homological algebra, is essential. For Chapter 10, basic algebraic geometry and sheaf cohomology are required. Throughout the text, a diverse range of exercises of varying difficulty are interspersed, enhancing the depth of topical comprehension.

The overarching theme of this book revolves around the structure and representation theory of infinite-dimensional locally reductive Lie algebras and superalgebras. Chapters 1 to 6 establish the foundational framework, while the final 4 chapters delve into specialized topics within the broader field. Lie superalgebras and flag supermanifolds are explored in Chapters 3, 7, and 10, and readers can choose to skip these chapters based on their interests.

Weight: 553g
Dimension: 235 x 155 (mm)
ISBN-13: 9783030896591
Edition number: 1st ed. 2022